Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1852 conjugacy classes of subgroups; only the 558 normal subgroups are shown.
This group has 1852 conjugacy classes of subgroups — too many to draw. Only its 558 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3×#3746 | C2 | direct (N × H) |
| 4. C22×#3746 | C3 | direct (N × H) |
| 11. C3×#3746 | C22 | direct (N × H) |
| 17. C2×#3746 | C2×C3 | direct (N × H) |
| 40. #3746 | C22×C3 | direct (N × H) |
| 42. C22×C33 | Q16 | semidirect |
| 73. C2×C33 | C2×Q16 | semidirect |
| 91. C22×C32 | Dic12 | semidirect |
| 92. C22×C32 | C3×Q16 | semidirect |
| 106. C33 | C22×Q16 | semidirect |
| 127. C2×C32 | C2×Dic12 | semidirect |
| 128. C2×C32 | C2×C3×Q16 | semidirect |
| 139. C22×C3 | C3×Dic12 | semidirect |
| 140. C22×C3 | #3746 | direct (N × H) |
| 152. C32 | C22×Dic12 | semidirect |
| 153. C32 | C22×C3×Q16 | semidirect |
| 163. C2×C3 | C2×C3×Dic12 | semidirect |
| 164. C2×C3 | C2×#3746 | direct (N × H) |
| 167. C22 | C3×#3746 | direct (N × H) |
| 173. C3 | C22×C3×Dic12 | semidirect |
| 174. C3 | C22×#3746 | direct (N × H) |
| 175. C2 | C2×C3×#3746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#634 | 2 |
| C22×C33×C8 | 2 |
| C2×C3×#3746 | 2 |
| C22×#3746 | 3 |
| C22×C3×Dic12 | 3 |